Summary: It is known that a scene consisting of \(k\) convex polyhedra of total complexity \(n\) has at most \(O(n^4 k^2)\) distinct orthographic views, and that the number of such views is \(\Omega((nk^2 + n^2)^2)\) in the worst case. The corresponding bounds for perspective views are \(O(n^6 k^3)\) and \(\Omega((nk^2 + n^2)^3)\), respectively. In this paper, we close these gaps by improving the lower bounds. We construct an example of a scene with \(\Theta(n^4 k^2)\) orthographic views, and another with \(\Theta(n^6 k^3)\) perspective views. Our construction can also be used to improve the known lower bounds for the number of silhouette views and for the number of distinct views from a viewpoint moving along a straight line.
For the entire collection see [Zbl 0968.00054].